Is (sec(α))(sec(α))=tan(α) ?

The answer to whether (sec(α))(sec(α))=tan(α) is False

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prove (sec(α))(sec(α))=tan(α)

prove

(sec (α)) (sec (α)) = tan (α)

False

Solution steps

sec (α) sec (α) = tan (α)

Show that the two sides are not equal

For

sec (α) sec (α) = tan (α)

plug in

α = 0

sec (0) sec (0) = 1

sec (0) sec (0)

Use the following trivial identity:

sec (0) = 1

sec (0)

sec (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 1

= 1 \cdot 1

Simplify

= 1

tan (0) = 0

tan (0)

Use the following trivial identity:

tan (0) = 0

tan (0)

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 0

= 0

The two sides are not equal

\Rightarrow False

cos^{2} (2 x) + sin^{2} (2 x) = 1

sec (x) \cdot sin (x) = tan (x)

(1 - cos (θ)) (1 + sec (θ)) = sec (θ) - cos (θ)

tan (x) csc (x) sec (x) = tan^{2} (x) + 1

\frac{( csc ^{2} ( x ) - 1 )}{csc ^{2} ( x )} = cos^{2} (x)

Is (sec(α))(sec(α))=tan(α) ?
The answer to whether (sec(α))(sec(α))=tan(α) is False